Micro-scale modelling of bovine cortical bone fracture: Analysis of crack propagation and microstructure using X-FEM

Bone-fracture susceptibility is increased by factors such as bone loss, microstructure changes, and variations in material properties. Therefore, investigation of the effect of microstructure and material properties of bone on crack propagation in it and of its global response at macro-scale is important. A non-uniform distribution of osteons in a cortical bone tissue results in a localization of deformation processes. Such localization can affect bone’s performance under external loads and initiate fracture or assist its propagation. Once the fracture initiates, that distribution can play an important role in the crack propagation process at micro-scale; subsequently, the global response at macro-scale could also be affected. In this study, a two-dimensional numerical (finite-element) fracture model for osteonal bovine cortical bone was developed with account for its microstructure using extended finite element method (X-FEM). The topology of a transverse-radial cross section of a bovine cortical bone was captured using optical microscopy. Mechanical properties for the bone’s micro-structural features in the cross section were obtained with a use of the nanoindentation technique. Both the topology and nanoindentation data were used as input to the model formulated with the Abaqus finite-element software. The area, directly reflecting micro-scale information, was embedded into the region with homogenised properties of the cortical bone. Numerical simulations provide the macro-scale global response, crack propagation paths and distribution of maximum principal stress at the microscopic level for three different topologies – homogeneous, three-phase composite and four-phase composite model under tensile loading conditions. The calculated stress fields for various cases of topologies demonstrate different patterns due to implementation of micro-structural features in the finite-element models, confirming an important role of the microstructure in the crack propagation scenarios. The suggested approach emphasizes the importance of micro-structural features, especially cement lines, in development of bone failure.